116 ideas
| 13466 | We are all post-Kantians, because he set the current agenda for philosophy [Hart,WD] |
| Full Idea: We are all post-Kantians, ...because Kant set an agenda for philosophy that we are still working through. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Hart says that the main agenda is set by Kant's desire to defend the principle of sufficient reason against Hume's attack on causation. I would take it more generally to be the assessment of metaphysics, and of a priori knowledge. |
| 19250 | Everything interesting should be recorded, with records that can be rearranged [Peirce] |
| Full Idea: Everything worth notice is worth recording; and those records should be so made that they can readily be arranged, and particularly so that they can be rearranged. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: Yet another epigraph for my project! Peirce must have had a study piled with labelled notes, and he would have adored this database, at least in its theory. |
| 19228 | Sciences concern existence, but philosophy also concerns potential existence [Peirce] |
| Full Idea: Philosophy differs from the special sciences in not confining itself to the reality of existence, but also to the reality of potential being. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: One might reply that sciences also concern potential being, if their output is universal generalisations (such as 'laws'). I take disposition and powers to be central to existence, which are hence of interest to sciences. |
| 13477 | The problems are the monuments of philosophy [Hart,WD] |
| Full Idea: The real monuments of philosophy are its problems. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Presumably he means '....rather than its solutions'. No other subject would be very happy with that sort of claim. Compare Idea 8243. A complaint against analytic philosophy is that it has achieved no consensus at all. |
| 19241 | An idea on its own isn't an idea, because they are continuous systems [Peirce] |
| Full Idea: There is no such thing as an absolutely detached idea. It would be no idea at all. For an idea is itself a continuous system. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: This is the new anti-epigraph for this database. This idea is part of Peirce's idea that relations are the central feature of our grasp of the world. |
| 19227 | Philosophy is a search for real truth [Peirce] |
| Full Idea: Philosophy differs from mathematics in being a search for real truth. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: This is important, coming from the founder of pragmatism, in rejecting the anti-realism which a lot of modern pragmatists seem to like. |
| 19218 | Metaphysics is pointless without exact modern logic [Peirce] |
| Full Idea: The metaphysician who is not prepared to grapple with the difficulties of modern exact logic had better put up his shutters and go out of the trade. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: This announcement comes before Russell proclaimed mathematical logic to be the heart of metaphysics (though it is contemporary with Frege's work, of which Peirce was unaware). It places Peirce firmly in the analytic tradition. |
| 16241 | The metaphysics of nature should focus on physics [Maudlin] |
| Full Idea: Metaphysics, insofar as it is concerned with the natural world, can do no better than to reflect on physics. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: I suppose so. Physics only works at one level of description. Metaphysics often works with concepts which only emerge at a more general level than physics. There are also many metaphysical problems which are of no interest to most physicists. |
| 19229 | Metaphysics is the science of both experience, and its general laws and types [Peirce] |
| Full Idea: Metaphysics is the science of being, not merely as given in physical experience, but of being in general, its laws and types. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: I agree with this. The question then is whether such a science is possible. Dogmatic empiricists think not. Explanatory empiricists (me) think it is. |
| 19219 | Metaphysical reasoning is simple enough, but the concepts are very hard [Peirce] |
| Full Idea: Metaphysical reasonings, such as they have hitherto been, have been simple enough for the most part. It is the metaphysical concepts which it is difficult to apprehend. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: Peirce is not, of course, saying that it is just conceptual, because for him science comes first. It is the woolly concepts that alienate some people from metaphysics. Metaphysicians should challenge the concepts they use much, much more! |
| 16257 | Kant survives in seeing metaphysics as analysing our conceptual system, which is a priori [Maudlin] |
| Full Idea: The Kantian strain survives in the notion that metaphysics is not about the world, but about our 'conceptual system', especially as what structures our thought about the world. This keeps it a priori, and so not about the world itself. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3) | |
| A reaction: Strawson would embody this view, I suppose. I take our conceptual system to be largely a reflection of (and even creation of) the world, and not just an arbitrary conventional attempt to grasp the world. Analysing concepts partly analyses the world. |
| 16276 | Wide metaphysical possibility may reduce metaphysics to analysis of fantasies [Maudlin] |
| Full Idea: If metaphysical possibility extends more widely than physical possibility, this may make metaphysics out to be nothing but the analysis of fantastical descriptions produced by philosophers. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: Maudlin wants metaphysics to be firmly constrained in its possibilities by what scientific undestanding permits, and he is right. Metaphysics must integrate into science, or wither away on the margins. |
| 19231 | Metaphysics is turning into logic, and logic is becoming mathematics [Peirce] |
| Full Idea: Metaphysics is gradually and surely taking on the character of a logic. And finally seems destined to become more and more converted into mathematics. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: Remarkably prescient for 1898. I don't think Peirce knew of Frege (and certainly not when he wrote this). It shows that the revolution of Frege and Russell was in the air. It's there in Dedekind's writings. Peirce doesn't seem to be a logicist. |
| 13515 | To study abstract problems, some knowledge of set theory is essential [Hart,WD] |
| Full Idea: By now, no education in abstract pursuits is adequate without some familiarity with sets. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: A heart-sinking observation for those who aspire to study metaphysics and modality. The question is, what will count as 'some' familiarity? Are only professional logicians now allowed to be proper philosophers? |
| 16244 | If the universe is profligate, the Razor leads us astray [Maudlin] |
| Full Idea: If the universe has been profligate, then Ockham's Razor will lead us astray. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: That is, there may be a vast number of entities which exist beyond what seems to be 'necessary'. |
| 16255 | The Razor rightly prefers one cause of multiple events to coincidences of causes [Maudlin] |
| Full Idea: The Razor is good when it councils higher credence to explanations which posit a single cause to multiple events that occur in a striking pattern, over explanations involving coincidental multiple causes. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: This is in the context of Maudlin warning against embracing the Razor too strongly. Presumably inductive success suggests that the world supports this particular use of the Razor. |
| 19247 | The one unpardonable offence in reasoning is to block the route to further truth [Peirce] |
| Full Idea: To set up a philosophy which barricades the road of further advance toward the truth is the one unpardonable offence in reasoning. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: This is Popper's rather dubious objection to essentialism in science. Yet Popper tried to do the same thing with his account of induction. |
| 13469 | Tarski showed how we could have a correspondence theory of truth, without using 'facts' [Hart,WD] |
| Full Idea: It is an ancient and honourable view that truth is correspondence to fact; Tarski showed us how to do without facts here. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This is a very interesting spin on Tarski, who certainly seems to endorse the correspondence theory, even while apparently inventing a new 'semantic' theory of truth. It is controversial how far Tarski's theory really is a 'correspondence' theory. |
| 19246 | 'Holding for true' is either practical commitment, or provisional theory [Peirce] |
| Full Idea: Whether or not 'truth' has two meanings, I think 'holding for true' has two kinds. One is practical holding for true which alone is entitled to the name of Belief; the other is the acceptance of a proposition, which in pure science is always provisional. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: The problem here seems to be that we can act on a proposition without wholly believing it, like walking across thin ice. |
| 13504 | Truth for sentences is satisfaction of formulae; for sentences, either all sequences satisfy it (true) or none do [Hart,WD] |
| Full Idea: We explain truth for sentences in terms of satisfaction of formulae. The crux here is that for a sentence, either all sequences satisfy it or none do (with no middle ground). For formulae, some sequences may satisfy it and others not. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This is the hardest part of Tarski's theory of truth to grasp. |
| 13503 | A first-order language has an infinity of T-sentences, which cannot add up to a definition of truth [Hart,WD] |
| Full Idea: In any first-order language, there are infinitely many T-sentences. Since definitions should be finite, the agglomeration of all the T-sentences is not a definition of truth. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: This may be a warning shot aimed at Davidson's extensive use of Tarski's formal account in his own views on meaning in natural language. |
| 13500 | Conditional Proof: infer a conditional, if the consequent can be deduced from the antecedent [Hart,WD] |
| Full Idea: A 'conditional proof' licenses inferences to a conditional from a deduction of its consequent from its antecedent. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: That is, a proof can be enshrined in an arrow. |
| 13502 | ∃y... is read as 'There exists an individual, call it y, such that...', and not 'There exists a y such that...' [Hart,WD] |
| Full Idea: When a quantifier is attached to a variable, as in '∃(y)....', then it should be read as 'There exists an individual, call it y, such that....'. One should not read it as 'There exists a y such that...', which would attach predicate to quantifier. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: The point is to make clear that in classical logic the predicates attach to the objects, and not to some formal component like a quantifier. |
| 13456 | Set theory articulates the concept of order (through relations) [Hart,WD] |
| Full Idea: It is set theory, and more specifically the theory of relations, that articulates order. | |
| From: William D. Hart (The Evolution of Logic [2010]) | |
| A reaction: It would seem that we mainly need set theory in order to talk accurately about order, and about infinity. The two come together in the study of the ordinal numbers. |
| 13497 | Nowadays ZFC and NBG are the set theories; types are dead, and NF is only useful for the whole universe [Hart,WD] |
| Full Idea: The theory of types is a thing of the past. There is now nothing to choose between ZFC and NBG (Neumann-Bernays-Gödel). NF (Quine's) is a more specialized taste, but is a place to look if you want the universe. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13443 | ∈ relates across layers, while ⊆ relates within layers [Hart,WD] |
| Full Idea: ∈ relates across layers (Plato is a member of his unit set and the set of people), while ⊆ relates within layers (the singleton of Plato is a subset of the set of people). This distinction only became clear in the 19th century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: Getting these two clear may be the most important distinction needed to understand how set theory works. |
| 13442 | Without the empty set we could not form a∩b without checking that a and b meet [Hart,WD] |
| Full Idea: Without the empty set, disjoint sets would have no intersection, and we could not form a∩b without checking that a and b meet. This is an example of the utility of the empty set. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: A novice might plausibly ask why there should be an intersection for every pair of sets, if they have nothing in common except for containing this little puff of nothingness. But then what do novices know? |
| 13493 | In the modern view, foundation is the heart of the way to do set theory [Hart,WD] |
| Full Idea: In the second half of the twentieth century there emerged the opinion that foundation is the heart of the way to do set theory. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: It is foundation which is the central axiom of the iterative conception of sets, where each level of sets is built on previous levels, and they are all 'well-founded'. |
| 13495 | Foundation Axiom: an nonempty set has a member disjoint from it [Hart,WD] |
| Full Idea: The usual statement of Foundation is that any nonempty set has a member disjoint from it. This phrasing is ordinal-free and closer to the primitives of ZFC. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13461 | We can choose from finite and evident sets, but not from infinite opaque ones [Hart,WD] |
| Full Idea: When a set is finite, we can prove it has a choice function (∀x x∈A → f(x)∈A), but we need an axiom when A is infinite and the members opaque. From infinite shoes we can pick a left one, but from socks we need the axiom of choice. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The socks example in from Russell 1919:126. |
| 13462 | With the Axiom of Choice every set can be well-ordered [Hart,WD] |
| Full Idea: It follows from the Axiom of Choice that every set can be well-ordered. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: For 'well-ordered' see Idea 13460. Every set can be ordered with a least member. |
| 13516 | If we accept that V=L, it seems to settle all the open questions of set theory [Hart,WD] |
| Full Idea: It has been said (by Burt Dreben) that the only reason set theorists do not generally buy the view that V = L is that it would put them out of business by settling their open questions. | |
| From: William D. Hart (The Evolution of Logic [2010], 10) | |
| A reaction: Hart says V=L breaks with the interative conception of sets at level ω+1, which is countable is the constructible view, but has continuum many in the cumulative (iterative) hierarch. The constructible V=L view is anti-platonist. |
| 13441 | Naďve set theory has trouble with comprehension, the claim that every predicate has an extension [Hart,WD] |
| Full Idea: 'Comprehension' is the assumption that every predicate has an extension. Naďve set theory is the theory whose axioms are extensionality and comprehension, and comprehension is thought to be its naivety. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: This doesn't, of course, mean that there couldn't be a more modest version of comprehension. The notorious difficulty come with the discovery of self-referring predicates which can't possibly have extensions. |
| 13494 | The iterative conception may not be necessary, and may have fixed points or infinitely descending chains [Hart,WD] |
| Full Idea: That the iterative sets suffice for most of ZFC does not show they are necessary, nor is it evident that the set of operations has no fixed points (as 0 is a fixed point for square-of), and no infinitely descending chains (like negative integers). | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: People don't seem to worry that they aren't 'necessary', and further measures are possible to block infinitely descending chains. |
| 13457 | A 'partial ordering' is irreflexive and transitive; the sets are ordered, but not the subsets [Hart,WD] |
| Full Idea: We say that a binary relation R 'partially orders' a field A just in case R is irreflexive (so that nothing bears R to itself) and transitive. When the set is {a,b}, its subsets {a} and {b} are incomparable in a partial ordering. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13458 | A partial ordering becomes 'total' if any two members of its field are comparable [Hart,WD] |
| Full Idea: A partial ordering is a 'total ordering' just in case any two members of its field are comparable, that is, either a is R to b, or b is R to a, or a is b. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: See Idea 13457 for 'partial ordering'. The three conditions are known as the 'trichotomy' condition. |
| 13490 | Von Neumann defines α<β as α∈β [Hart,WD] |
| Full Idea: One of the glories of Von Neumann's theory of numbers is to define α < β to mean that α ∈ β. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13460 | 'Well-ordering' must have a least member, so it does the natural numbers but not the integers [Hart,WD] |
| Full Idea: A total order 'well-orders' its field just in case any nonempty subset B of its field has an R-least member, that is, there is a b in B such that for any a in B different from b, b bears R to a. So less-than well-orders natural numbers, but not integers. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) | |
| A reaction: The natural numbers have a starting point, but the integers are infinite in both directions. In plain English, an order is 'well-ordered' if there is a starting point. |
| 13481 | Maybe sets should be rethought in terms of the even more basic categories [Hart,WD] |
| Full Idea: Some have claimed that sets should be rethought in terms of still more basic things, categories. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: [He cites F.William Lawvere 1966] It appears to the the context of foundations for mathematics that he has in mind. |
| 19237 | Deduction is true when the premises facts necessarily make the conclusion fact true [Peirce] |
| Full Idea: The question of whether a deductive argument is true or not is simply the question whether or not the facts stated in the premises could be true in any sort of universe no matter what be true without the fact stated in the conclusion being true likewise. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: A remarkably modern account, fitting the normal modern view of semantic consequence, and expressing the necessity in the validity in terms of something close to possible worlds. |
| 19256 | Our research always hopes that reality embodies the logic we are employing [Peirce] |
| Full Idea: Every attempt to understand anything at least hopes that the very objects of study themselves are subject to a logic more or less identical with that which we employ. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII) | |
| A reaction: The idea that external objects might be subject to a logic has become very unfashionable since Frege, but I love the idea. I'm inclined to think that we derive our logic from the world, so I'm a bit more confident that Peirce. |
| 19238 | The logic of relatives relies on objects built of any relations (rather than on classes) [Peirce] |
| Full Idea: In the place of the class ...the logic of relatives considers the system, which is composed of objects brought together by any kind of relations whatsoever. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: Peirce's logic of relations might support the purely structural view of reality defended by Ladyman and Ross. Modern logic standardly expresses its semantics in terms of set theory. Peirce pioneered relations in logic. |
| 13506 | The universal quantifier can't really mean 'all', because there is no universal set [Hart,WD] |
| Full Idea: All the main set theories deny that there is a set of which everything is a member. No interpretation has a domain with everything in it. So the universal quantifier never gets to mean everything all at once; 'all' does not mean all. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: Could you have an 'uncompleted' universal set, in the spirit of uncompleted infinities? In ordinary English we can talk about 'absolutely everything' - we just can't define a set of everything. Must we 'define' our domain? |
| 13513 | Models are ways the world might be from a first-order point of view [Hart,WD] |
| Full Idea: Models are ways the world might be from a first-order point of view. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13505 | Model theory studies how set theory can model sets of sentences [Hart,WD] |
| Full Idea: Modern model theory investigates which set theoretic structures are models for which collections of sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: So first you must choose your set theory (see Idea 13497). Then you presumably look at how to formalise sentences, and then look at the really tricky ones, many of which will involve various degrees of infinity. |
| 13511 | Model theory is mostly confined to first-order theories [Hart,WD] |
| Full Idea: There is no developed methematics of models for second-order theories, so for the most part, model theory is about models for first-order theories. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13512 | Modern model theory begins with the proof of Los's Conjecture in 1962 [Hart,WD] |
| Full Idea: The beginning of modern model theory was when Morley proved Los's Conjecture in 1962 - that a complete theory in a countable language categorical in one uncountable cardinal is categorical in all. | |
| From: William D. Hart (The Evolution of Logic [2010], 9) |
| 13496 | First-order logic is 'compact': consequences of a set are consequences of a finite subset [Hart,WD] |
| Full Idea: First-order logic is 'compact', which means that any logical consequence of a set (finite or infinite) of first-order sentences is a logical consequence of a finite subset of those sentences. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13484 | Berry's Paradox: we succeed in referring to a number, with a term which says we can't do that [Hart,WD] |
| Full Idea: Berry's Paradox: by the least number principle 'the least number denoted by no description of fewer than 79 letters' exists, but we just referred to it using a description of 77 letters. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: I struggle with this. If I refer to 'an object to which no human being could possibly refer', have I just referred to something? Graham Priest likes this sort of idea. |
| 13482 | The Burali-Forti paradox is a crisis for Cantor's ordinals [Hart,WD] |
| Full Idea: The Burali-Forti Paradox was a crisis for Cantor's theory of ordinal numbers. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13507 | The machinery used to solve the Liar can be rejigged to produce a new Liar [Hart,WD] |
| Full Idea: In effect, the machinery introduced to solve the liar can always be rejigged to yield another version the liar. | |
| From: William D. Hart (The Evolution of Logic [2010], 4) | |
| A reaction: [He cites Hans Herzberger 1980-81] The machinery is Tarski's device of only talking about sentences of a language by using a 'metalanguage'. |
| 13459 | The less-than relation < well-orders, and partially orders, and totally orders the ordinal numbers [Hart,WD] |
| Full Idea: We can show (using the axiom of choice) that the less-than relation, <, well-orders the ordinals, ...and that it partially orders the ordinals, ...and that it totally orders the ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13463 | There are at least as many infinite cardinals as transfinite ordinals (because they will map) [Hart,WD] |
| Full Idea: Since we can map the transfinite ordinals one-one into the infinite cardinals, there are at least as many infinite cardinals as transfinite ordinals. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13491 | The axiom of infinity with separation gives a least limit ordinal ω [Hart,WD] |
| Full Idea: The axiom of infinity with separation yields a least limit ordinal, which is called ω. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13492 | Von Neumann's ordinals generalise into the transfinite better, because Zermelo's ω is a singleton [Hart,WD] |
| Full Idea: It is easier to generalize von Neumann's finite ordinals into the transfinite. All Zermelo's nonzero finite ordinals are singletons, but if ω were a singleton it is hard to see how if could fail to be the successor of its member and so not a limit. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) |
| 13446 | 19th century arithmetization of analysis isolated the real numbers from geometry [Hart,WD] |
| Full Idea: The real numbers were not isolated from geometry until the arithmetization of analysis during the nineteenth century. | |
| From: William D. Hart (The Evolution of Logic [2010], 1) |
| 13509 | We can establish truths about infinite numbers by means of induction [Hart,WD] |
| Full Idea: Mathematical induction is a way to establish truths about the infinity of natural numbers by a finite proof. | |
| From: William D. Hart (The Evolution of Logic [2010], 5) | |
| A reaction: If there are truths about infinities, it is very tempting to infer that the infinities must therefore 'exist'. A nice, and large, question in philosophy is whether there can be truths without corresponding implications of existence. |
| 13474 | Euclid has a unique parallel, spherical geometry has none, and saddle geometry has several [Hart,WD] |
| Full Idea: There is a familiar comparison between Euclid (unique parallel) and 'spherical' geometry (no parallel) and 'saddle' geometry (several parallels). | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 13471 | Mathematics makes existence claims, but philosophers usually say those are never analytic [Hart,WD] |
| Full Idea: The thesis that no existence proposition is analytic is one of the few constants in philosophical consciences, but there are many existence claims in mathematics, such as the infinity of primes, five regular solids, and certain undecidable propositions. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) |
| 19226 | We now know that mathematics only studies hypotheses, not facts [Peirce] |
| Full Idea: It did not become clear to mathematicians before modern times that they study nothing but hypotheses without as pure mathematicians caring at all how the actual facts may be. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: 'Modern' here is 1898. As a logical principle this would seem to qualify as 'if-thenism' (see alphabetical themes). It's modern descendant might be modal structuralism (see Geoffrey Hellman). It take maths to be hypotheses abstracted from experience. |
| 16243 | The Humean view is wrong; laws and direction of time are primitive, and atoms are decided by physics [Maudlin] |
| Full Idea: The Humean project is unjustified, in that both the laws of nature and the direction of time require no analysis, and is misconceived, in that the atoms it employs do not correspond to present physical ontology. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: I certainly find it strange, or excessively empirical, that Lewis thinks our account of reality should rest on 'qualities'. Maudlin's whole books is an implicit attack on David Lewis. |
| 16271 | Lewis says it supervenes on the Mosaic, but actually thinks the Mosaic is all there is [Maudlin] |
| Full Idea: At base it is not merely, as Lewis says, that everything else supervenes on the Mosaic; but rather that anything that exists at all is just a feature or element or generic property of the Mosaic. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: [Maudlin has just quoted Idea 16210] Correct about Lewis, but Lewis just has a normal view of supervenience. Only 'emergentists' would think the supervenience allowed anything more, and they are deeply misguided, and in need of help. |
| 16273 | If the Humean Mosaic is ontological bedrock, there can be no explanation of its structure [Maudlin] |
| Full Idea: The Humean Mosaic appears to admit of no further explanation. Since it is the ontological bedrock, …none of the further things can account for the structure of the Mosaic itself. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: A very nice point, reminiscent of Popper's objection to essentialism, that he thought it blocked further enquiry, when actually further enquiry was possible. Lewis and Hume seem too mesmerised by epistemology. They need best explanation. |
| 16275 | The 'spinning disc' is just impossible, because there cannot be 'homogeneous matter' [Maudlin] |
| Full Idea: The 'spinning disc' is not metaphysically possible. We have every reason to believe that there is no such thing as 'perfectly homogeneous matter'. The atomic theory of matter is as well established as any scientific theory is likely to be. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: This is a key case for Maudlin, and his contempt for metaphysics which is not scientifically informed. I agree with him. Extreme thought experiments are worth considering, but impossible ones are pointless. |
| 13488 | Mass words do not have plurals, or numerical adjectives, or use 'fewer' [Hart,WD] |
| Full Idea: Jespersen calls a noun a mass word when it has no plural, does not take numerical adjectives, and does not take 'fewer'. | |
| From: William D. Hart (The Evolution of Logic [2010], 3) | |
| A reaction: Jespersen was a great linguistics expert. |
| 19240 | Realism is the belief that there is something in the being of things corresponding to our reasoning [Peirce] |
| Full Idea: If there is any reality, then it consists of this: that there is in the being of things something which corresponds to the process of reasoning. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: A nice definition of realism, a little different from usual. I belief that the normal logic of daily thought corresponds (in its rules and connectives) to the way the world is. We evaluate success in logic by truth-preservation. |
| 19239 | There may be no reality; it's just our one desperate hope of knowing anything [Peirce] |
| Full Idea: What is reality? Perhaps there isn't any such thing at all. It is but a working hypothesis which we try, our one desperate forlorn hope of knowing anything. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: I'm not quite sure why the hope is 'forlorn'. We have no current reason to doubt that the hypothesis is working out extremely well. Lovely idea, though. |
| 16258 | To get an ontology from ontological commitment, just add that some theory is actually true [Maudlin] |
| Full Idea: The doctrine of ontological commitment becomes a central element in a theory of ontology if one merely adds that a particular theory is, in fact, true | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: Helpful. I don't think the truth of a theory entails the actual existence of every component mentioned in the theory, as some of them may be generalisations, abstractions, vague, or even convenient linking fictions. |
| 16259 | Naďve translation from natural to formal language can hide or multiply the ontology [Maudlin] |
| Full Idea: Naďve translation from natural language into formal language can obscure necessary ontology as easily as it can create superfluous ontological commitment. …The lion's share of metaphysical work is done when settling on the right translation. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: I suspect this is more than a mere problem of 'naivety', but may be endemic to the whole enterprise. If you hammer a square peg into a round hole, you expect to lose something. Language is subtle, logic is crude. |
| 16253 | A property is fundamental if two objects can differ in only that respect [Maudlin] |
| Full Idea: Fragility is not a fundamental physical property, in that two pieces of glass cannot be physically identical save for their fragility. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: Nice. The best idea I have found in Maudlin, so far! This gives a very nice test for picking out the fundamental physical and intrinsic properties. |
| 16263 | Fundamental physics seems to suggest there are no such things as properties [Maudlin] |
| Full Idea: If one believes that fundamental physics is the place to look for the truths about universals (or tropes or natural sets), then one may find that physics is telling us there are no such things. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.2) | |
| A reaction: His prior discussion of quantum chromodynamics suggests, to me, merely that properties can be described in terms of vectors etc., and remains neutral on the ontology - but then I am blinded by science. |
| 16260 | Existence of universals may just be decided by acceptance, or not, of second-order logic [Maudlin] |
| Full Idea: On one line of thought, the question of whether universals exist seems to reduce to the question of the utility, or necessity, of using second-order rather than first-order logic. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 3.1) | |
| A reaction: Second-order logic quantifies over properties, where first-order logic just quantifies over objects. This is an extreme example of doing your metaphysics largely through logic. Not my approach. |
| 16277 | Logically impossible is metaphysically impossible, but logically possible is not metaphysically possible [Maudlin] |
| Full Idea: While logical impossibility is a species of metaphysical impossibility, logical possibility is not a species of metaphysical possibility. The logically impeccable description 'Cicero was not Tully' describes a metaphysically impossible situation. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 7 Epilogue) | |
| A reaction: The context of this is Maudlin attack on daft notions of metaphysical possibility that are at variance with the limits set by science, but he is still conceding that there are types of metaphysical modality. |
| 19252 | Objective chance is the property of a distribution [Peirce] |
| Full Idea: Chance, as an objective phenomenon, is a property of a distribution. ...In order to have any meaning, it must refer to some definite arrangement of all the things. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VI) |
| 19232 | In ordinary language a conditional statement assumes that the antecedent is true [Peirce] |
| Full Idea: In our ordinary use of language we always understand the range of possibility in such a sense that in some possible case the antecedent shall be true. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Peirce is discussing Diodorus, and proposes the view nowadays defended by Edgington, though in the end Peirce defends the standard material conditional as simpler. I suspect that this discussion by Peirce is not well known. |
| 16249 | A counterfactual antecedent commands the redescription of a selected moment [Maudlin] |
| Full Idea: The purpose of the antecedent of a counterfactual is to provide instructions on how to pick a Cauchy surface (pick a moment in time) and how to generate an altered description of that moment. It is more of a command than an indicative sentence. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: Quite plausible, but the antecedent might contain no description. 'If things had gone differently, we wouldn't be in this mess'. The antecedent might be timeless. 'If pigs had wings, they still wouldn't fly'. |
| 19223 | We act on 'full belief' in a crisis, but 'opinion' only operates for trivial actions [Peirce] |
| Full Idea: 'Full belief' is willingness to upon a proposition in vital crises, 'opinion' is willingness to act on it in relatively insignificant affairs. But pure science has nothing at all to do with action. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: A nice clear statement of the pragmatic view of beliefs. It is not much help in distinguishing full belief about the solar system from mere opinion about remote galaxies. Ditto for historical events. |
| 13480 | Fregean self-evidence is an intrinsic property of basic truths, rules and definitions [Hart,WD] |
| Full Idea: The conception of Frege is that self-evidence is an intrinsic property of the basic truths, rules, and thoughts expressed by definitions. | |
| From: William D. Hart (The Evolution of Logic [2010], p.350) | |
| A reaction: The problem is always that what appears to be self-evident may turn out to be wrong. Presumably the effort of arriving at a definition ought to clarify and support the self-evident ingredient. |
| 13476 | The failure of key assumptions in geometry, mereology and set theory throw doubt on the a priori [Hart,WD] |
| Full Idea: In the case of the parallels postulate, Euclid's fifth axiom (the whole is greater than the part), and comprehension, saying was believing for a while, but what was said was false. This should make a shrewd philosopher sceptical about a priori knowledge. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: Euclid's fifth is challenged by infinite numbers, and comprehension is challenged by Russell's paradox. I can't see a defender of the a priori being greatly worried about these cases. No one ever said we would be right - in doing arithmetic, for example. |
| 19253 | We talk of 'association by resemblance' but that is wrong: the association constitutes the resemblance [Peirce] |
| Full Idea: Allying certain ideas like 'crimson' and 'scarlet' is called 'association by resemblance'. The name is not a good one, since it implies that resemblance causes association, while in point of fact it is the association which constitutes the resemblance. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII) | |
| A reaction: I take it that Hume would have agreed with this. It is an answer to Russell's claim that 'resemblance' must itself be a universal. |
| 19224 | Scientists will give up any conclusion, if experience opposes it [Peirce] |
| Full Idea: The scientific man is not in the least wedded to his conclusions. He risks nothing upon them. He stands ready to abandon one or all as experience opposes them. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: In the age of massive speculative research grants, the idea that 'he risks nothing upon them' is no longer true. Ditto for building aircraft and bridges, which are full of theoretical science. Notoriously, many scientists don't live up to Peirce's idea. |
| 19243 | If each inference slightly reduced our certainty, science would soon be in trouble [Peirce] |
| Full Idea: Were every probable inference less certain than its premises, science, which piles inference upon inference, often quite deeply, would soon be in a bad way. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: This seems to endorse Aristotle's picture of demonstration about scientific and practical things as being a form of precise logic, rather than progressive probabilities. Our generalisations may be more certain than the particulars they rely on. |
| 19225 | I classify science by level of abstraction; principles derive from above, and data from below [Peirce] |
| Full Idea: I classify the sciences on Comte's general principles, in order of the abstractness of their objects, so that each science may largely rest for its principles upon those above it in the scale, while drawing its data in part from those below it. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: He places mathematics at the peak of abstraction. I assume physics is more abstract than biology. So chemistry draws principles from physics and data from biology. Not sure about this. Probably need to read Comte on it. |
| 16254 | Induction leaps into the unknown, but usually lands safely [Maudlin] |
| Full Idea: Induction is always a leap beyond the known, but we are constantly assured by later experience that we have landed safely. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 2.5) | |
| A reaction: Not philosophically very interesting, but a nice remark for capturing the lived aspect of inductive thought, as practised by the humblest of animals. |
| 19234 | 'Induction' doesn't capture Greek 'epagoge', which is singulars in a mass producing the general [Peirce] |
| Full Idea: The word 'inductio' is Cicero's imitation of Aristotle's term 'epagoge'. It fails to convey the full significance of the Greek word, which implies the examples are arrayed and brought forward in a mass. 'The assault upon the generals by the singulars'. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Interesting, thought I don't think there is enough evidence in Aristotle to get the Greek idea fully clear. |
| 19236 | Induction can never prove that laws have no exceptions [Peirce] |
| Full Idea: Induction can never afford the slightest reason to think that a law is without an exception. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Part of the general Humean doubts about induction, but very precisely stated, and undeniable. You can then give up on universal laws, or look for deeper reasons to justify your conviction that there are no exceptions. E.g. observe mass, or Higgs Boson. |
| 19251 | The worst fallacy in induction is generalising one recondite property from a sample [Peirce] |
| Full Idea: The most dangerous fallacy of inductive reasoning consists in examining a sample, finding some recondite property in it, and concluding at once that it belongs to the whole collection. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: The point, I take it, is not that you infer that the whole collection has all the properties of the sample, but that some 'recondite' or unusual property is sufficiently unusual to be treated as general. |
| 19235 | How does induction get started? [Peirce] |
| Full Idea: Induction can never make a first suggestion. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: This seems to lead to the general modern problem of the 'theory-laden' nature of observation. You don't see anything at all without some idea of what you are looking for. How do you spot the 'next instance'. Instance of what? Nice. |
| 16245 | Laws should help explain the things they govern, or that manifest them [Maudlin] |
| Full Idea: A law ought to be capable of playing some role in explaining the phenomena that are governed by or are manifestations of it. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.2) | |
| A reaction: I find this attitude bewildering. 'Why do electrons have spin?' 'Because they all do!' The word 'governed' is the clue. What on earth is a law, if it can 'govern' nature? What is its ontological status? Natures of things are basic, not 'laws'. |
| 19222 | Men often answer inner 'whys' by treating unconscious instincts as if they were reasons [Peirce] |
| Full Idea: Men many times fancy that they act from reason, when the reasons they attribute to themselves are nothing but excuses which unconscious instinct invents to satisfy the teasing 'whys' of the ego. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: A strikely modern thought, supported by a lot of modern neuro-science and psychology. It is crucial to realise that we don't have to accept the best explanation we can think of. |
| 19220 | We may think animals reason very little, but they hardly ever make mistakes! [Peirce] |
| Full Idea: Those whom we are so fond of referring to as the 'lower animals' reason very little. Now I beg you to observe that those beings very rarely commit a mistake, while we ---- ! | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: We might take this as pessimism about reason, but I would take it as inviting a much broader view of rationality. I think nearly all animal behaviour is highly rational. Are animals 'sensible' in what they do? Their rationality is unadventurous. |
| 19255 | Generalisation is the great law of mind [Peirce] |
| Full Idea: The generalising tendency is the great law of mind. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII) | |
| A reaction: How else could a small and compact mind get a grip on a vast and diverse reality? This must even apply to inarticulate higher animals. |
| 19242 | Generalization is the true end of life [Peirce] |
| Full Idea: Generalization, the spelling out of continuous systems, in thought, in sentiment, in deed, is the true end of life. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], III) | |
| A reaction: I take understanding to be the true aim of life, and full grasp of particulars (e.g. of particular people) is as necessary as generalisation. This is still a very nice bold idea. |
| 19249 | 'Know yourself' is not introspection; it is grasping how others see you [Peirce] |
| Full Idea: 'Know thyself' does not mean instrospect your soul. It means see yourself as others would see you if they were intimate enough with you. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: When it comes to anger management, I would have thought that introspection had some use. You can see a tantrum coming before even your intimates can. Nice disagreement with Sartre! (Idea 7123) |
| 19257 | Whatever is First must be sentient [Peirce] |
| Full Idea: I think that what is First is ipso facto sentient. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VIII) | |
| A reaction: He doesn't mention Leibniz's monads, but that looks like the ancestor of Peirce's idea. He doesn't make clear (here) how far he would take the idea. I would just say that whatever is 'First' must be active rather than passive. |
| 19248 | Reasoning involves observation, experiment, and habituation [Peirce] |
| Full Idea: The mental operations concerning in reasoning are three. The first is Observation; the second is Experimentation; and the third is Habituation. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], V) | |
| A reaction: I like the breadth of this. Even those who think scientific reasoning has priority over logic (as I do, thinking of it as the evaluation of evidence, with Sherlock Holmes as its role model) will be surprised to finding observation and habituation there. |
| 19221 | Everybody overrates their own reasoning, so it is clearly superficial [Peirce] |
| Full Idea: The very fact that everybody so ridiculously overrates his own reasoning, is sufficient to show how superficial the faculty is. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: A nice remark. The obvious counter-thought is that the collective reasoning of mankind really has been rather impressive, even though people haven't yet figured out how to live at peace with one another. |
| 13475 | The Fregean concept of GREEN is a function assigning true to green things, and false to the rest [Hart,WD] |
| Full Idea: A Fregean concept is a function that assigns to each object a truth value. So instead of the colour green, the concept GREEN assigns truth to each green thing, but falsity to anything else. | |
| From: William D. Hart (The Evolution of Logic [2010], 2) | |
| A reaction: This would seem to immediately hit the renate/cordate problem, if there was a world in which all and only the green things happened to be square. How could Frege then distinguish the green from the square? Compare Idea 8245. |
| 19233 | Indexicals are unusual words, because they stimulate the hearer to look around [Peirce] |
| Full Idea: Words like 'this', 'that', 'I', 'you', enable us to convey meanings which words alone are incompetent to express; they stimulate the hearer to look about him. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], II) | |
| A reaction: Peirce was once of the first to notice the interest of indexicals, and this is a very nice comment on them. A word like 'Look!' isn't like the normal flow of verbiage, and may be the key to indexicals. |
| 19230 | People should follow what lies before them, and is within their power [Peirce] |
| Full Idea: Each person ought to select some definite duty that clearly lies before him and is well within his power as the special task of his life. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], I) | |
| A reaction: I like that. Note especially that it should be 'well' within his power. Note also that this is a 'duty', and not just a friendly suggestion. Not sure what the basis of the duty is. |
| 19245 | We are not inspired by other people's knowledge; a sense of our ignorance motivates study [Peirce] |
| Full Idea: It is not the man who thinks he knows it all, that can bring other men to feel their need for learning, and it is only a deep sense that one is miserably ignorant that can spur one on in the toilsome path of learning. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) |
| 19244 | Chemists rely on a single experiment to establish a fact; repetition is pointless [Peirce] |
| Full Idea: The chemist contents himself with a single experiment to establish any qualitative fact, because he knows there is such a uniformity in the behavior of chemical bodies that another experiment would be a mere repetition of the first in every respect. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], IV) | |
| A reaction: I take it this endorses my 'Upanishads' view of natural kinds - that for each strict natural kind, if you've seen one you've them all. This seems to fit atoms and molecules, but only roughly fits tigers. |
| 16248 | Evaluating counterfactuals involves context and interests [Maudlin] |
| Full Idea: The evaluation of counterfactual claims is widely recognised as being influenced by context and interest. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: Such evaluation certainly seems to involve imagination, and so the pragmatics can creep in there. I don't quite see why it should be deeply contextual. |
| 16250 | We don't pick a similar world from many - we construct one possibility from the description [Maudlin] |
| Full Idea: It seems unlikely the psychological process could mirror Lewis's semantics: people don't imagine a multiplicity of worlds and the pick out the most similar. Rather we construct representations of possible worlds from counterfactual descriptions. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.5) | |
| A reaction: I approve of fitting such theories into a psychology, but this may be unfair to Lewis, who aims for a logical model, not an account of how we actually approach the problem. |
| 16268 | The counterfactual is ruined if some other cause steps in when the antecedent fails [Maudlin] |
| Full Idea: A counterexample to the counterfactual approach is that perhaps the effect would have occurred despite the absence of the cause since another cause would have stepped in to bring it about. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: …Hence you cannot say 'if C had not occurred, E would definitely not have occurred'. You have to add 'ceteris paribus', which ruins the neatness of the theory. |
| 16267 | If we know the cause of an event, we seem to assent to the counterfactual [Maudlin] |
| Full Idea: When we think we know the cause of an event, we typically assent to the corresponding Hume counterfactual. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: This is the correct grounding of the counterfactual approach - not that we think counterfactuals are causation, but that knowledge of causation will map neatly onto a network of counterfactuals, thus providing a logic for the whole process. |
| 16269 | If the effect hadn't occurred the cause wouldn't have happened, so counterfactuals are two-way [Maudlin] |
| Full Idea: If Kennedy had still been President in Dec 1963, he would not have been assassinated in Nov 1963, so the counterfactual goes both ways (where the cause seems to only go one way). | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5) | |
| A reaction: Maudlin says a lot of fine-tuning has sort of addressed these problems, but that counterfactual causation is basically wrong-headed anyway, and I incline to agree, though one must understand what the theory is (and is not) trying to do. |
| 19254 | Our laws of nature may be the result of evolution [Peirce] |
| Full Idea: We may suppose that the laws of nature are results of an evolutionary process. ...But this evolution must proceed according to some principle: and this principle will itself be of the nature of a law. | |
| From: Charles Sanders Peirce (Reasoning and the Logic of Things [1898], VII) | |
| A reaction: Maybe I've missed something, but this seems a rather startling idea that doesn't figure much in modern discussions of laws of nature. Lee Smolin's account of evolving universes comes to mind. |
| 16242 | Laws of nature are ontological bedrock, and beyond analysis [Maudlin] |
| Full Idea: The laws of nature stand in no need of 'philosophical analysis'; they ought to be posited as ontological bedrock. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], Intro) | |
| A reaction: This is Maudlin's most basic principle, and I don't agree with it. The notion that laws are more deeply embedded in reality than the physical stuff they control is a sort of 'law-mysticism' that needs to be challenged. |
| 16247 | Laws are primitive, so two indiscernible worlds could have the same laws [Maudlin] |
| Full Idea: Laws are ontologically primitives at least in that two worlds could differ in their laws but not in any observable respect. ….[21] I take content of the laws to be expressed by equations. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.4) | |
| A reaction: At least that spells out his view fairly dramatically, but I am baffled as to what he thinks a law could be. He is arguing against the Lewis regularity-axioms view, and the Armstrong universal-relations view. He ignores the essentialist view. |
| 16272 | Fundamental laws say how nature will, or might, evolve from some initial state [Maudlin] |
| Full Idea: The fundamental laws of nature appear to be laws of temporal evolution: they specify how the state of the universe will, or might, evolve from a given intial state. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 6) | |
| A reaction: Maudlin takes both laws of nature and the passage of time to be primitive facts, and this is how they are connected. I think (this week) that I take time and causation to be primitive, but not laws. |
| 16251 | 'Humans with prime house numbers are mortal' is not a law, because not a natural kind [Maudlin] |
| Full Idea: 'All humans who live in houses with prime house numbers are mortal' is not a law because the class referred to is not a natural kind. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 1.6) | |
| A reaction: Maudlin wants laws to be primitive, but he now needs a primitive notion of a natural kind to make it work. If kinds generate laws, you can ditch the laws, and build your theory on the kinds. He also says no death is explained by 'all humans are mortal'. |
| 16270 | If laws are just regularities, then there have to be laws [Maudlin] |
| Full Idea: On the Mill-Ramsey-Lewis account of laws, I take it that if the world is extensive and variegated enough, then there must be laws. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 5.2) | |
| A reaction: A nice point. If there is any sort of pattern discernible in the surface waves on the sea, then there must be a law to cover it, not matter how vague or complex. |
| 16264 | I believe the passing of time is a fundamental fact about the world [Maudlin] |
| Full Idea: I believe that it is a fundamental, irreducible fact about the spatio-temporal structure of the world that time passes. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4) | |
| A reaction: Worth quoting because it comes from a philosopher fully informed about, and heavily committed to, the physicist's approach to reality. One fears that physicists steeped in Einstein are all B-series Eternalists. Get a life! |
| 16265 | If time passes, presumably it passes at one second per second [Maudlin] |
| Full Idea: It is necessary and, I suppose, a priori that if time passes at all it passes at one second per second. …Similarly, the fair exchange rate for a dollar must be a dollar. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4.1) | |
| A reaction: [He is discussing Huw Price on time] This is a reply to the claim that if time passes it has to pass at some rate, and 'one second per second' is ridiculous. Not very convincing, even with the dollar analogy. |
| 16266 | There is one ordered B series, but an infinitude of A series, depending on when the present is [Maudlin] |
| Full Idea: Given events ordered in a B series, one defines an infinitude of different A series that correspond to taking different events as 'now' or 'present'. McTaggart talks of 'the A series' when there is an infinitude of such. | |
| From: Tim Maudlin (The Metaphysics within Physics [2007], 4.3 n11) | |
| A reaction: This strikes me as a rather mathematical (and distorted) claim about the A series view. The A-series is one dynamic happening. Not an infinity of static times lines, each focused on a different 'now'. |